arXiv subjects

Harpreet S. Dhillon

Publications and source records attributed to Harpreet S. Dhillon.

At least 145 records · Page 8Linked to original sources

arXiv2017

Serving Distance and Coverage in a Closed Access PHP-Based Heterogeneous Cellular Network

Heterogeneous cellular networks (HCNs) usually exhibit spatial separation amongst base stations (BSs) of different types (termed tiers in this paper). For instance, operators will usually not deploy a picocell in close proximity to a macrocell, thus inducing separation amongst the locations of pico and macrocells. This separation has recently been captured by modeling the small cell locations by a Poisson Hole Process (PHP) with the hole centers being the locations of the macrocells. Due to the presence of exclusion zones, the analysis of the resulting model is significantly more complex compared to the more popular Poisson Point Process (PPP) based models. In this paper, we derive a tight bound on the distribution of the distance of a typical user to the closest point of a PHP. Since the exact distribution of this distance is not known, it is often approximated in the literature. For this model, we then provide tight characterization of the downlink coverage probability for a typical user in a two-tier closed-access HCN under two cases: (i) typical user is served by the closest macrocell, and (ii) typical user is served by its closest small cell. The proposed approach can be extended to analyze other relevant cases of interest, e.g., coverage in a PHP-based open access HCN.

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arXiv2017

Effect of Retransmissions on Optimal Caching in Cache-enabled Small Cell Networks

Caching popular content in the storage of small cells is being considered as an efficient technique to complement limited backhaul of small cells in ultra-dense heterogeneous cellular networks. Limited storage capacity of the small cells renders it important to determine the optimal set of files (cache) to be placed on each small cell. In contrast to prior works on optimal caching, in this work we study the effect of retransmissions on the optimal cache placement policy for both static and mobile user scenarios. With the popularity of files modeled as a Zipf distribution and a maximum n transmissions, i.e., n-1 retransmissions, allowed to receive each file, we determine the optimal caching probability of the files that maximizes the hit probability. Our closed-form optimal solutions concretely demonstrate that the optimal caching probabilities are very sensitive to the number of retransmissions.

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arXiv2017

Poisson Cluster Process: Bridging the Gap Between PPP and 3GPP HetNet Models

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated the need to consider variety of user and base station (BS) configurations for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models considered by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry based approach modeling the user and BS locations as independent and homogeneous Poisson point processes (PPPs) has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based model is not rich enough to capture all the spatial configurations that appear in real world HetNet deployments (on which 3GPP simulation models are based). In this paper, we bridge the gap between the 3GPP simulation models and the popular PPP-based analytical model by developing a new unified HetNet model in which a fraction of users and some BS tiers are modeled as Poisson cluster processes (PCPs). This model captures both non-uniformity and coupling in the BS and user locations. For this setup, we derive exact expression for downlink coverage probability under maximum signal-to-interference ratio (SIR) cell association model. As intermediate results, we define and evaluate sum-product functionals for PPP and PCP. Special instances of the proposed model are shown to closely resemble different configurations considered in 3GPP HetNet models. Our results concretely demonstrate that the performance trends are highly sensitive to the assumptions made on the user and SBS configurations.

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arXiv2017

Effect of User Mobility on the Performance of Device-to-Device Networks with Distributed Caching

We consider a distributed caching device-to-device (D2D) network in which a user's file of interest is cached as several portions in the storage of other devices in the network. Assuming that the user needs to obtain all these file portions, the portions cached farther away naturally become the performance bottleneck. This is due to the fact that dominant interferers may be closer to the receiver than the serving device. Using a simple stochastic geometry model, we concretely demonstrate that this bottleneck can be loosened if the users are mobile. Gains obtained from mobility are quantified in terms of coverage probability.

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arXiv2017

Downlink Coverage Analysis for a Finite 3D Wireless Network of Unmanned Aerial Vehicles

In this paper, we consider a finite network of unmanned aerial vehicles (UAVs) serving a given region. Modeling this network as a uniform binomial point process (BPP), we derive the downlink coverage probability of a reference receiver located at an arbitrary position on the ground assuming Nakagami-$m$ fading for all wireless links. The reference receiver is assumed to connect to its closest transmitting node as is usually the case in cellular systems. After deriving the distribution of distances from the reference receiver to the serving and interfering nodes, we derive an exact expression for downlink coverage probability in terms of the derivative of Laplace transform of interference power distribution. In the downlink of this system, it is not unusual to encounter scenarios in which the line-of-sight (LOS) component is significantly stronger than the reflected multipath components. To emulate such scenarios, we also derive the coverage probability in the absence of fading from the results of Nakagami-$m$ fading by taking the limit $m \to \infty$. Using asymptotic expansion of incomplete gamma function, we concretely show that this limit reduces to a redundant condition. Consequently, we derive an accurate coverage probability approximation for this case using dominant interferer-based approach in which the effect of dominant interferer is exactly captured and the residual interference from other interferers is carefully approximated. We then derive the bounds of the approximate coverage probability using Berry-Esseen theorem. Our analyses reveal several useful trends in coverage probability as a function of height of the transmitting nodes and the location of reference receiver on the ground.

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arXiv2016

A Primer on Cellular Network Analysis Using Stochastic Geometry

This tutorial is intended as an accessible but rigorous first reference for someone interested in learning how to model and analyze cellular network performance using stochastic geometry. In particular, we focus on computing the signal-to-interference-plus-noise ratio (SINR) distribution, which can be characterized by the coverage probability (the SINR CCDF) or the outage probability (its CDF). We model base stations (BSs) in the network as a realization of a homogeneous Poisson point process of density $λ$, and compute the SINR for three main cases: the downlink, uplink, and finally the multi-tier downlink, which is characterized by having $k$ tiers of BSs each with a unique density $λ_i$ and transmit power $p_i$. These three baseline results have been extensively extended to many different scenarios, and we conclude with a brief summary of some of those extensions.

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arXiv2016

A Comprehensive Analysis of 5G Heterogeneous Cellular Systems operating over $κ$-$μ$ Shadowed Fading Channels

Emerging cellular technologies such as those proposed for use in 5G communications will accommodate a wide range of usage scenarios with diverse link requirements. This will include the necessity to operate over a versatile set of wireless channels ranging from indoor to outdoor, from line-of-sight (LOS) to non-LOS, and from circularly symmetric scattering to environments which promote the clustering of scattered multipath waves. Unfortunately, many of the conventional fading models adopted in the literature to develop network models lack the flexibility to account for such disparate signal propagation mechanisms. To bridge the gap between theory and practical channels, we consider $κ$-$μ$ shadowed fading, which contains as special cases, the majority of the linear fading models proposed in the open literature, including Rayleigh, Rician, Nakagami-m, Nakagami-q, One-sided Gaussian, $κ$-$μ$, $η$-$μ$, and Rician shadowed to name but a few. In particular, we apply an orthogonal expansion to represent the $κ$-$μ$ shadowed fading distribution as a simplified series expression. Then using the series expressions with stochastic geometry, we propose an analytic framework to evaluate the average of an arbitrary function of the SINR over $κ$-$μ$ shadowed fading channels. Using the proposed method, we evaluate the spectral efficiency, moments of the SINR, bit error probability and outage probability of a $K$-tier HetNet with $K$ classes of BSs, differing in terms of the transmit power, BS density, shadowing characteristics and small-scale fading. Building upon these results, we provide important new insights into the network performance of these emerging wireless applications while considering a diverse range of fading conditions and link qualities.

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arXiv2016

Nearest-Neighbor and Contact Distance Distributions for Thomas Cluster Process

We characterize the statistics of nearest-neighbor and contact distance distributions for Thomas cluster process (TCP), which is a special case of Poisson cluster process. In particular, we derive the cumulative distribution function (CDF) of the distance to the nearest point of TCP from a reference point for three different cases: (i) reference point is not a part of the point process, (ii) it is chosen uniformly at random from the TCP, and (iii) it is a randomly chosen point from a cluster chosen uniformly at random from the TCP. While the first corresponds to the contact distance distribution, the other two provide two different viewpoints for the nearest-neighbor distance distribution.

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arXiv2016

Fundamentals of Modeling Finite Wireless Networks using Binomial Point Process

Modeling the locations of nodes as a uniform binomial point process (BPP), we present a generic mathematical framework to characterize the performance of an arbitrarily-located reference receiver in a finite wireless network. Different from most of the prior works where the serving transmitter (TX) node is located at the fixed distance from the reference receiver, we consider two general TX-selection policies: i) uniform TX-selection: the serving node is chosen uniformly at random amongst transmitting nodes, and ii) k-closest TX-selection: the serving node is the k-th closest node out of transmitting nodes to the reference receiver. The key intermediate step in our analysis is the derivation of a new set of distance distributions that lead not only to the tractable analysis of coverage probability but also enable the analyses of wide range of classical and currently trending problems in wireless networks. Using this new set of distance distributions, we first investigate the diversity loss due to SIR correlation in a finite network. We then obtain the optimal number of links that can be simultaneously activated to maximize network spectral efficiency. Finally, we evaluate optimal caching probability to maximize the total hit probability in cache-enabled finite networks.

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arXiv2016

Spatio-temporal Interference Correlation and Joint Coverage in Cellular Networks

This paper provides an analytical framework with foundations in stochastic geometry to characterize the spatio-temporal interference correlation as well as the joint coverage probability at two spatial locations in a cellular network. In particular, modeling the locations of cellular base stations (BSs) as a Poisson Point Process (PPP), we study interference correlation at two spatial locations $\ell_1$ and $\ell_2$ separated by a distance $v$, when the user follows \emph{closest BS association policy} at both spatial locations and moves from $\ell_1$ to $\ell_2$. With this user displacement, two scenarios can occur: i) the user is handed off to a new serving BS at $\ell_2$, or ii) no handoff occurs and the user is served by the same BS at both locations. After providing intermediate results such as probability of handoff and distance distributions of the serving BS at the two user locations, we use them to derive exact expressions for spatio-temporal interference correlation coefficient and joint coverage probability for any distance separation $v$. We also study two different handoff strategies: i) \emph{handoff skipping}, and ii) \emph{conventional handoffs}, and derive the expressions of joint coverage probability for both strategies. The exact analysis is not straightforward and involves a careful treatment of the neighborhood of the two spatial locations and the resulting handoff scenarios. To provide analytical insights, we also provide easy-to-use expressions for two special cases: i) static user ($v =0$) and ii) highly mobile user ($v \rightarrow \infty)$. As expected, our analysis shows that the interference correlation and joint coverage probability decrease with increasing $v$, with $v \rightarrow \infty$ corresponding to a completely uncorrelated scenario.

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arXiv2016

A Stochastic Geometric Analysis of Device-to-Device Communications Operating over Generalized Fading Channels

Device-to-device (D2D) communications are now considered as an integral part of future 5G networks which will enable direct communication between user equipment (UE) without unnecessary routing via the network infrastructure. This architecture will result in higher throughputs than conventional cellular networks, but with the increased potential for co-channel interference induced by randomly located cellular and D2D UEs. The physical channels which constitute D2D communications can be expected to be complex in nature, experiencing both line-of-sight (LOS) and non-LOS (NLOS) conditions across closely located D2D pairs. As well as this, given the diverse range of operating environments, they may also be subject to clustering of the scattered multipath contribution, i.e., propagation characteristics which are quite dissimilar to conventional Rayeligh fading environments. To address these challenges, we consider two recently proposed generalized fading models, namely $κ-μ$ and $η-μ$, to characterize the fading behavior in D2D communications. Together, these models encompass many of the most widely encountered and utilized fading models in the literature such as Rayleigh, Rice (Nakagami-$n$), Nakagami-$m$, Hoyt (Nakagami-$q$) and One-Sided Gaussian. Using stochastic geometry we evaluate the rate and bit error probability of D2D networks under generalized fading conditions. Based on the analytical results, we present new insights into the trade-offs between the reliability, rate, and mode selection under realistic operating conditions. Our results suggest that D2D mode achieves higher rates over cellular link at the expense of a higher bit error probability. Through numerical evaluations, we also investigate the performance gains of D2D networks and demonstrate their superiority over traditional cellular networks.

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arXiv2016

Optimal Geographic Caching in Finite Wireless Networks

Cache-enabled device-to-device (D2D) networks turn memory of the devices at the network edge, such as smart phones and tablets, into bandwidth by enabling asynchronous content sharing directly between proximate devices. Limited storage capacity of the mobile devices necessitates the determination of optimal set of contents to be cached on each device. In order to study the problem of optimal cache placement, we model the locations of devices in a finite region (e.g., coffee shop, sports bar, library) as a uniform binomial point process (BPP). For this setup, we first develop a generic framework to analyze the coverage probability of the target receiver (target-Rx) when the requested content is available at the $k^{th}$ closest device to it. Using this coverage probability result, we evaluate optimal caching probability of the popular content to maximize the total hit probability. Our analysis concretely demonstrates that optimal caching probability strongly depends on the number of simultaneously active devices in the network.

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arXiv2016

Fundamentals of Cluster-Centric Content Placement in Cache-Enabled Device-to-Device Networks

This paper develops a comprehensive analytical framework with foundations in stochastic geometry to characterize the performance of cluster-centric content placement in a cache-enabled device-to-device (D2D) network. Different from device-centric content placement, cluster-centric placement focuses on placing content in each cluster such that the collective performance of all the devices in each cluster is optimized. Modeling the locations of the devices by a Poisson cluster process, we define and analyze the performance for three general cases: (i)$k$-Tx case: receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at the $k^{th}$ closest device to the cluster center, (ii) $\ell$-Rx case: receiver of interest is the $\ell^{th}$ closest device to the cluster center and its content of interest is available at a device chosen uniformly at random from the same cluster, and (iii) baseline case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at a device chosen independently and uniformly at random from the same cluster. Easy-to-use expressions for the key performance metrics, such as coverage probability and area spectral efficiency (ASE) of the whole network, are derived for all three cases. Our analysis concretely demonstrates significant improvement in the network performance when the device on which content is cached or device requesting content from cache is biased to lie closer to the cluster center compared to baseline case. Based on this insight, we develop and analyze a new generative model for cluster-centric D2D networks that allows to study the effect of intra-cluster interfering devices that are more likely to lie closer to the cluster center.

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arXiv2016

Poisson Hole Process: Theory and Applications to Wireless Networks

Interference field in wireless networks is often modeled by a homogeneous Poisson Point Process (PPP). While it is realistic in modeling the inherent node irregularity and provides meaningful first-order results, it falls short in modeling the effect of interference management techniques, which typically introduce some form of spatial interaction among active transmitters. In some applications, such as cognitive radio and device-to-device networks, this interaction may result in the formation of holes in an otherwise homogeneous interference field. The resulting interference field can be accurately modeled as a Poisson Hole Process (PHP). Despite the importance of PHP in many applications, the exact characterization of interference experienced by a typical node in a PHP is not known. In this paper, we derive several tight upper and lower bounds on the Laplace transform of this interference. Numerical comparisons reveal that the new bounds outperform all known bounds and approximations, and are remarkably tight in all operational regimes of interest. The key in deriving these tight and yet simple bounds is to capture the local neighborhood around the typical point accurately while simplifying the far field to attain tractability. Ideas for tightening these bounds further by incorporating the effect of overlaps in the holes are also discussed. These results immediately lead to an accurate characterization of the coverage probability of the typical node in a PHP under Rayleigh fading.

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arXiv2015

Optimizing Data Aggregation for Uplink Machine-to-Machine Communication Networks

Machine-to-machine (M2M) communication's severe power limitations challenge the interconnectivity, access management, and reliable communication of data. In densely deployed M2M networks, controlling and aggregating the generated data is critical. We propose an energy efficient data aggregation scheme for a hierarchical M2M network. We develop a coverage probability-based optimal data aggregation scheme for M2M devices to minimize the average total energy expenditure per unit area per unit time or simply the {\em energy density} of an M2M communication network. Our analysis exposes the key tradeoffs between the energy density of the M2M network and the coverage characteristics for successive and parallel transmission schemes that can be either half-duplex or full-duplex. Comparing the rate and energy performances of the transmission models, we observe that successive mode and half-duplex parallel mode have better coverage characteristics compared to full-duplex parallel scheme. Simulation results show that the uplink coverage characteristics dominate the trend of the energy consumption for both successive and parallel schemes.

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arXiv2015

A Tractable Metric for Evaluating Base Station Geometries in Cellular Network Localization

In this letter, we present a new metric for characterizing the geometric conditions encountered in cellular positioning based on the angular spread of the base stations (BSs). The metric is shown to be closely related to the geometric-dilution-of-precision (GDOP), yet has the benefit of being characterizable in terms of the network parameters for BS layouts modeled according to a Poisson point process (PPP). As an additional benefit, the metric is shown to immediately yield a device's probability of being inside or outside the convex hull of the BSs, which localization researchers will widely-recognize as being a strong indicator of localization performance.

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arXiv2015

Towards a Tractable Analysis of Localization Fundamentals in Cellular Networks

When dedicated positioning systems, such as GPS, are unavailable, a mobile device has no choice but to fall back on its cellular network for localization. Due to random variations in the channel conditions to its surrounding base stations (BS), the mobile device is likely to face a mix of both favorable and unfavorable geometries for localization. Analytical studies of localization performance (e.g., using the Cramér-Rao lower bound) usually require that one fix the BS geometry, and favorable geometries have always been the preferred choice in the literature. However, not only are the resulting analytical results constrained to the selected geometry, this practice is likely to lead to overly-optimistic expectations of typical localization performance. Ideally, localization performance should be studied across all possible geometric setups, thereby also removing any selection bias. This, however, is known to be hard and has been carried out only in simulation. In this paper, we develop a new tractable approach where we endow the BS locations with a distribution by modeling them as a Poisson point process (PPP), and use tools from stochastic geometry to obtain easy-to-use expressions for key performance metrics. In particular, we focus on the probability of detecting some minimum number of BSs, which is shown to be closely coupled with a network operator's ability to obtain satisfactory localization performance (e.g., meet FCC E911 requirements). This metric is indifferent to the localization technique (e.g., TOA, TDOA, AOA, or hybrids thereof), though different techniques will presumably lead to different BS hearability requirements. In order to mitigate excessive interference due to the presence of dominant interferers in the form of other BSs, we incorporate both BS coordination and frequency reuse in the proposed framework and quantify the resulting performance gains analytically.

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arXiv2015

On Jamming Against Wireless Networks

In this paper, we study jamming attacks against wireless networks. Specifically, we consider a network of base stations (BS) or access points (AP) and investigate the impact of a fixed number of jammers that are randomly deployed according to a Binomial point process. We shed light on the network performance in terms of a) the outage probability and b) the error probability of a victim receiver in the downlink of this wireless network. We derive analytical expressions for both these metrics and discuss in detail how the jammer network must adapt to the various wireless network parameters in order to effectively attack the victim receivers. For instance, we will show that with only 1 jammer per BS/AP a) the outage probability of the wireless network can be increased from 1% (as seen in the non-jamming case) to 80% and b) when retransmissions are used, the jammers cause the effective network activity factor (and hence the interference among the BSs) to be doubled. Furthermore, we show that the behavior of the jammer network as a function of the BS/AP density is not obvious. In particular, an interesting concave-type behavior is seen which indicates that the number of jammers required to attack the wireless network must scale with the BS density only until a certain value beyond which it decreases. In the context of error probability of the victim receiver, we study whether or not some recent results related to jamming in the point-to-point link scenario can be extended to the case of jamming against wireless networks. Numerical results are presented to validate the theoretical inferences presented.

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